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Consider total cost and total revenue given in the following table:$$\mathrm{Quantity} \quad 0\quad 1\quad 2\quad 3\quad 4\quad 5\quad 6\quad 7 $$$$\mathrm{Total cost} \quad$8\quad 9\quad 10\quad 11\quad 13\quad 19\quad 27\quad 37 $$$$\mathrm{Total revenue}\quad $0\quad 8\quad 16\quad 24\quad 32\quad 40\quad 48\quad 56 $$a. Calculate profit for each quantity. How much should the firm produce to maximize profit?b. Calculate marginal revenue and marginal cost for each quantity. Graph them. ($Hint$: Put thepoints between whole numbers. For example, the marginal cost between 2 and 3 should be graphedat 2 $1\over2$.) At what quantity do these curves cross? How does this relate to your answer to part (a)?c. Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industryis in a long-run equilibrium?

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Okay, So the first part of the problem asked for us to calculate the profit for each quantity, Um And then ask us how much should affirm produced to maximize profit. Well, this is pretty simple. So what we can do is we're going to just subtract they total revenue less the total cost, and that's going to equal our profit. So for each one of these columns here, we're going to go through and calculate the profit. So let's do that right now. So for the first unit, if we produce zero units, then our total costs is eight. So we would get a profit of negative eight for that zero unit, but over here, all right. Total calls is nine. Total revenue is eight for still taking a loss. So that b negative one. All right, for our second unit. All right, now we're turning a profit, which have a profit of six. Total revenues on the third unit is twenty four minus eleven. So in that case, we will be making thirteen dollars profit above over to the next unit, and we will be making nineteen on the five twenty one six units, twenty one at seven units nineteen. Now what? You jump out to you right here. Is that the move from six units two seven. Unit gets us less profit. So a rationally minded, uh, business owner would never want to make this jump. You're losing money for every for the next unit you're producing. So what's the maximum amount of profit I could make? Twenty one dollars. So? Well, how much should have firm produced to maximize profit? Well, it shouldn't matter. It should produce six units of whatever, uh, item it is making. Okay. All right, so that's profit on being asked for marginal revenue and marginal calls for each quantity. So let's go ahead and do that. Um, when we think about marginal revenue, right. That's just saying, what is the, uh, revenue from producing the next output? Right. Next item. The marginal unit. So if we're moving from zero to one. Well, how much? What is the marginal gain and revenue there? Well, so we were We used to be making zero revenue. Now we're making eight, So the are marginal revenue in that case is eight. Okay, Well, what if we move from one to two? All right. That means we're now going to be moving from revenue of eight to sixteen. Ah, well, again are marginal revenues. Eight. Well, you should pick up on a pattern really quickly that if you go through and do every single one of these sure enough, the marginal revenue is eight at every turn. So what does this tell us? Well, for every extra unit this firm is producing, it is still getting the exact same revenue from that next unit. So what does that tell us? Well, this is a price taking firm. And what does that mean? If it's a price taking firm? Well, it's in a competitive market, which is goingto answer next point in, Ah, part B. But real quickly. Let's get back to it. Let's get in to our marginal cultural All right. Margin are marginal costs, right? That's what we're doing next. All right, so here is just the same thing. Moving community, You know, what is the difference in cost? So as we go from zero units toe one unit Marshall calls is one nine to ten. One eleven. All right, eleven to thirteen. A way out. Just when we're going from six units to seven notice that we have a big jump until on are marginal calls of ten. Okay, so that completes that part of the problem. Now we need to go over and graph this, and we're going to see something that picks up on this. So if we go over to our graph, you'LL notice if you plot this out correctly, that for our marginal calls, remember? Over here. One one, one one. All right, so we have this flat curve here. Heard the instruction that says we need to plot this in a line. So as we, uh, move past, what do we say? A cz. We moved from three units to four units. You'LL see that our mortal call starts increase. This intersects with our margin revenue, which we said wass Ah, flat eight for every unit. And this intersects that six. What does this have to do with one another? Well, notice that marginal revenue and marginal cost intersect right at the point where we know where we know that profit is maximized right there. That's where a profit was maximized. No surprise here that that is actually where these lines intersect. So like we mentioned earlier, it is in a competitive industry because we see this really flat marshal revenue curve. And then also, can we tell if this industry is in long run equal a gram when we actually can't tell? Because we have no information on long term entry and exit, So we do not know the answer to that question.

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